Regular Article
A Unified Calculus Using the Generalized Bernoulli Polynomials

https://doi.org/10.1006/jath.2000.3550Get rights and content
Under an Elsevier user license
open archive

Abstract

We introduce an α-calculus with the help of the generalized Bernoulli polynomials. The parameter α is the order of a Bessel function of the first kind. The differential α-calculus can be put in a general context where the concept of supporting function is an important tool for practical purposes. Our somewhat more restrictive point of view has the advantage of permitting a consistent definition of an α-integral with several interesting properties. It results in the possibility of expressing a remainder, in the aforementioned context, in a completely new form in our case.

Cited by (0)

Communicated by Mourad, Ismail

f1

E-mail: [email protected]

1

The author was supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0009331.